Question 1

write a slope intercept equation for a line passing through the point ( 4, -2 )that is parallel to the line 4x+7y= 9 . then write a second equation for a line passing through the point (4,-2) that is perpendicular to the line 4x + 7y = 9

write a slope intercept equation for a line passing through the point ( 4, -2 )that-example-1

Question 2

$\begin{gathered} \text{Parallel line} \\ P(4,-2) \\ 4x+7y=9 \\ 7y=9-4x \\ y=(-4x)/(7)+(9)/(7) \\ Two\text{ lines are parallel when they have the same slope} \\ y=(-4x)/(7)+b\text{ } \\ \text{with the point given we can calculate b} \\ -2=(-4\cdot(4))/(7)+b\text{ } \\ -2=(-16)/(7)+b \\ b=-2+(16)/(7) \\ b=(2)/(7) \\ y=(-4)/(7)x+(2)/(7) \\ 7y=-4x+2 \\ 7y+4x=2 \\ the\text{ equation for the parallel line is }4x+7y=2 \\ \text{perpendicular line} \\ P(4,-2) \\ 4x+7y=9 \\ 7y=9-4x \\ y=(-4x)/(7)+(9)/(7),\text{ slope 1 =}(-4)/(7) \\ Two\text{ lines are perpendicular when you multiply both slopes} \\ and\text{ you get -1} \\ -1=slope\text{ 1 }\cdot\text{ slope 2} \\ slope\text{ 2 =}\frac{-1}{\text{slope1}} \\ \\ slope\text{ 2 =}(-1)/(((-4)/(7))) \\ \\ slope\text{ 2 =}(7)/(4) \\ y=(7)/(4)x+b \\ P(4,-2) \\ -2=(7)/(4)\cdot(4)+b \\ -2=7+b \\ b=-2-7 \\ b=-9 \\ y=(7)/(4)x-9 \\ -(7)/(4)x+y=-9 \\ \\ the\text{ equation for the perpendicular line is }-(7)/(4)x+y=-9 \end{gathered}$

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